There's obviously an issue with accountability, if shareholders do not get to have meaningful input into decisions at the corporate level. I suspect that in a large number of cases it doesn't make much difference.
The problem is that in cases in which it does make a difference, we'll have some small group of insiders who are effectively controlling the corporation, and whether we like it or not, the rest of us are, at some level, stakeholders. In particular, there are cases in which shareholders would probably change management and end up with a new, more innovative group, and they simply can't, because of the way the shareholding is structured in that particular entity.